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anonymous
 5 years ago
What mathematical induction?
anonymous
 5 years ago
What mathematical induction?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0series of natural numbers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But, I no get (k+1) part

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1proving that if its true for one step; its true for every step

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for me you have to identify whta is the successor of 1, and it is 0, so 1 is the successor of k

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, if n=1 is true, then (k+1) should be true?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1you havent really asked that detailed of a question; youre keeping secrets

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The series of natural numbers, can all be defined if we know what we mean by the three terms "0," "number", and "successor." But we may go a step farther: we can define all the natural numbers if we know what we mean by "0" and "successor." It will help us to understand the difference between finite and infinite to see how this can be done, and why the method by which it is done cannot be extended beyond the finite. We will not yet consider how "0" and "successor" are to be defined: we will for the moment assume that we know what these terms mean, and show how thence all other natural numbers can be obtained.

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Have you seen a domino effect? that's how you should think about induction.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oops, didn't know you needed example. I sorry :) I give you example :) One moment, please

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01 + 2 + 3 + . . . + n = ½n(n + 1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The logic is: It's true for n= (for example) 1 AND you can prove truth for n=k implies truth for n=k+1) THEN It's true for n = 1, 2, 3.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1n(n+1)  ah yes 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0[Oh fun fact that isn't why Gauss is famous]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Translating INewton logic into domino logic: How to make all the domino fall. 1) Make sure the 1st domino fall. 2) Make sure that whenever the kth domino fall, the (k+1)th domino fall as well. If you can ensure that then all dominos will fall :).

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1n=2; 1+2 = 3 ; 2(2+1)/2 = 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0............ THAT GREAT IDEA!!!!! :DDDDD

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1its why I know gauss tho lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1n = 3; 1+2+3 = 6 ; 3(3+1)/2 = 12/2 = 6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Gauss Fact #1: Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Gauss field equations

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Gauss Fact #2: Gauss checked the infinity of primes by counting them, starting from the last. Gauss Fact #3: Gauss considers infinity as the first nontrivial case in a proof by induction.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[ \text{Assume } \sum^k_{r=1}r = \frac{k(k+1)}{2}\] \[ \text{Assume } \sum^{k+1}_{r=1}r = \sum^k_{r=1}r + (k+1) = \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1)+2(k+1)}{2} \] \[=\frac{(k+1)[(k+1)+1]}{2} \] By mathematical induction blah...

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1I think the second word of "assume" shouldn't be there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It shouldn't, lazy copy and past, ugh.... sorry.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0paste*. I should have used \[\implies \] to start that line.
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